In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method...In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method. These schemes will be subjected to accuracy and stability tests before being used. Efficacy and robustness of the techniques under consideration will be demonstrated using an exact solution, one-Gausson, as well as conserved quantities. Interaction of two-soliton will be conducted. The numerical findings revealed, the interplay behavior is flexible.展开更多
In the paper,we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions.We first construct two model equations which include the high order dispersion and a seco...In the paper,we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions.We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity.And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept.Our mathematical tool is the logarithmic trial equation method.展开更多
文摘In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method. These schemes will be subjected to accuracy and stability tests before being used. Efficacy and robustness of the techniques under consideration will be demonstrated using an exact solution, one-Gausson, as well as conserved quantities. Interaction of two-soliton will be conducted. The numerical findings revealed, the interplay behavior is flexible.
文摘In the paper,we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions.We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity.And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept.Our mathematical tool is the logarithmic trial equation method.
